diff --git a/Lib/imaplib.py b/Lib/imaplib.py
index 1b375465af6..e020747e6ce 100644
--- a/Lib/imaplib.py
+++ b/Lib/imaplib.py
@@ -260,6 +260,7 @@ class IMAP4:
     def shutdown(self):
         """Close I/O established in "open"."""
         self.file.close()
+        self.sock.shutdown(socket.SHUT_RDWR)
         self.sock.close()
 
 
diff --git a/Lib/test/test_imaplib.py b/Lib/test/test_imaplib.py
index db07dd577bd..58e432ae634 100644
--- a/Lib/test/test_imaplib.py
+++ b/Lib/test/test_imaplib.py
@@ -220,6 +220,7 @@ class RemoteIMAPTest(unittest.TestCase):
 
     def test_logout(self):
         rs = self.server.logout()
+        self.server = None
         self.assertEqual(rs[0], 'BYE')
 
 
diff --git a/Misc/ACKS b/Misc/ACKS
index 0311ae96870..4a36b6dd16f 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -121,6 +121,7 @@ Tony Campbell
 Brett Cannon
 Mike Carlton
 Terry Carroll
+Lorenzo M. Catucci
 Donn Cave
 Per Cederqvist
 Octavian Cerna
diff --git a/Misc/NEWS b/Misc/NEWS
index 18938605465..9f18bbd9b4f 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -143,6 +143,9 @@ C-API
 Library
 -------
 
+- Issue #4471: Properly shutdown socket in IMAP.shutdown().  Patch by
+  Lorenzo M. Catucci.
+
 - Fix IMAP.login() to work properly.
 
 - Issue #10126: Fix distutils' test_build when Python was built with